Gravitational radiation from a particle in circular orbit around a black hole. V. Black-hole absorption and tail corrections

TL;DR

This paper analyzes gravitational wave energy loss from a particle orbiting a black hole, quantifying black-hole absorption effects and tail corrections, and compares perturbation theory with post-Newtonian methods.

Contribution

It provides a detailed calculation of energy loss including black-hole absorption and tail effects, and compares different wave-generation formalisms.

Findings

Black-hole absorption is a small effect, approximately proportional to v^8.

The total energy loss includes contributions both to infinity and absorbed by the black hole.

Tail corrections significantly affect the gravitational-wave field at large distances.

Abstract

A particle of mass $\mu$ moves on a circular orbit of a nonrotating black hole of mass $M$. Under the restrictions $\mu/M \ll 1$ and $v \ll 1$, where $v$ is the orbital velocity, we consider the gravitational waves emitted by such a binary system. We calculate $\dot{E}$, the rate at which the gravitational waves remove energy from the system. The total energy loss is given by $\dot{E} = \dot{E}^\infty + \dot{E}^H$, where $\dot{E}^\infty$ denotes that part of the gravitational-wave energy which is carried off to infinity, while $\dot{E}^H$ denotes the part which is absorbed by the black hole. We show that the black-hole absorption is a small effect: $\dot{E}^H/\dot{E} \simeq v^8$. We also compare the wave generation formalism which derives from perturbation theory to the post-Newtonian formalism of Blanchet and Damour. Among other things we consider the corrections to the asymptotic gravitational-wave field which are due to wave-propagation (tail) effects.